MI5 is investigating a British company with close ties to an alleged Russian spy amid concerns that its accounts may have been used to transfer funds for espionage to Britain.

Southern Union was set up by Anna Chapman – one of 10 people accused of being part of a Russian spy ring – and her husband Alex to wire money from Zimbabwe.

Now counter-intelligence officers are examining the company and a number of related bank accounts, the Guardian has learned. The revelation follows claims that Ms Chapman's father was an alleged KGB agent living in Zimbabwe at the time.

The inquiries come after a week in which the extraordinary claims of a New York espionage ring have focused on Ms Chapman, the 28-year-old whose Russian name was Anya Kushchenko.

It can also be disclosed that she was a friend of both a member of the House of Lords, who is a pre-eminent QC, and a head of one of the world's leading jewellery firms.

Alex Chapman, who was married to her for three years, has said Southern Union was a charity set up in 2002 by the couple to enable Zimbabwean expats to wire money back home at competitive rates. The company was set up by a millionaire South African friend of Anna's father who then took a commission, he said. Company documents filed by Ms Chapman show her signature.

The 30-year-old trainee psychiatrist has said his wife told him her father, Vasily Kushchenko, was a high-ranking KGB official living in Zimbabwe. "Towards the end of our marriage, she became very secretive, going for meetings of her own with 'Russian friends' and I guess it might have been because she was in contact with the Russian government," he told today's Daily Telegraph.

"[Her father] was scary. He would never introduce me to other Russian people who came to the house and he always seemed to have a lot more security than other diplomats," he said.

It was during her 'London years' from 2002 to 2007 that Chapman underwent her meteoric evolution from callow girl to the sort of sophisticated young woman who moves easily across the most influential and wealthy echelons of society.

Nicholas Camilleri, chief executive of the Mayfair-based hedge fund company Navigator Asset Management Advisers, said when he first met Chapman in 2005, she was, he said, "a 'green, wet behind the ears' type of girl".

But less than two years later, Chapman was being wined and dined at Annabel's and Cipriani in the company of Vincent Tchenguiz, a private equity billionaire.

Born in 1982 to Irina and Vasily Kushchenko, a diplomat who served as Russian ambassador in Kenya, Chapman seemed to have learned none of her father's urbanity by the time she first came to London.

"When I met her, she didn't know which way was up," said her husband, then a 21-year-old British student who met Chapman at a 2002 Docklands rave and married her in Moscow a few months later. The couple settled in Britain and lived quietly for the next two years. But then, Alex Chapman said, his wife began to change.

In 2005, he said, she began having meetings with people she referred to as "Russian friends".

"She was transformed into someone with access to a lot of money, boasting about all the influential people she was meeting," he said.

Later that year, Chapman left her husband and had moved into a cramped, two-bedroom flat behind Marble Arch tube station with Elena, her flatmate. She began seeing a French man, Laurent Tailleur, and moved in with him in 2007.

She lived frugally, friends said, and had no money. Chapman must have thought the privations were worth it. She was, after all, steadily sliding up the social scale that would soon see her attending glittering social functions such as the War and Peace Ball at the Dorchester.

Camilleri remembers the moment he met Chapman. It was in Cipriani, the Mayfair restaurant, and Chapman was with the London socialite, Shoshana Dadoun.

"I met Anya because I joined Shoshana's table one evening and she introduced me to her," said Camilleri. "I sat down and almost immediately, Anya asked if I could give her a job. She was very forward about it but that's how she was. She said she was working for Barclays Bank but wanted to leave," he said.

Chapman's audacity paid off. A few weeks later, she had exchanged the bank job which she said made her feel like a "slave" for the post of PA at Camilleri's glamorous, west London offices.

But those who knew her then struggle to see signs of the "practised deceiver" described by US prosecutors in court this week. "She was a simple girl," said Camilleri. "She was all about parties and didn't seem that bright. She wasn't constructive in her work, she just sat at her computer and booked my business trips."

Her husband, however, describes his former wife as "extremely intelligent", and claims she has an IQ of 162. She graduated in 2004 with a first-class honours degree in economics despite having to shuttle back and forth between Russia and London to complete the course.

Wayne Sharpe, executive chairman and founder of Bartercard, a trading exchange firm, also met Chapmen in 2005 at various social events. "The business people [in attendance] were the highest lot. She was in that set well and truly," he said. "She was very intelligent, attractive, personable and very articulate in English. She certainly was a great networker. She constantly ingratiated herself with all of the high-end businessmen Nicholas introduced her to."

The Guardian has learned that Southern Union is facing a second investigation following a complaint from its sole director that he was appointed to the position without his knowledge.

Steve Sugden, 36, claims that he had never heard of the firm until contacted by journalists and has reported the enterprise to Companies House, the body which enforces company law.

Two addresses are given for Sugden in the documents. One is a flat in Stoke Newington where the Chapmans once lived. The other is an address in Ireland.

Sugden, a telecoms salesman, said today that he has never been a company director, has never to the best of his knowledge met either of the Chapmans and has never been to Ireland.

He examined the company documents and recognised his date of birth, but said that the addresses and signature given were not his.

"This appears to be identity theft. I want the authorities to look into this because of who these people seem to be connected with," he said.

Sugden, from Tunbridge Wells, Kent, who is a father of two, added: "This is ridiculous. I have got my mates saying I am a Russian spy. But in truth I am currently liable for any debts this company runs up. I hadn't heard of it until yesterday."

The Guardian was unable to contact Mr Chapman today for comment on the company.

A spokesman for Companies House confirmed that they had received a verbal complaint from Sugden and said that the body is planning to launch an investigation into Southern Union once they receive a written complaint.

"We are in correspondence with Mr Sugden and will conduct an investigation subject to him confirming in writing information that he has given to us over the telephone. At the present time, he is the sole director of this company and any liabilities that might apply in the case would be his to resolve," he said.